Scientific Research

Time-distance helioseismology is a powerful method to study the interior of the Sun by computing travel time of individual acoustic wave packets as they travel through the Sun between two spatially separated locations on its surface. I have contributed to the theoretical development of this field.

Some important contributions include, (a) a theorem that forbids the use of certain methods used in computing travel time, (b) noting a phenomenon that makes the time-distance diagram lose its uniqueness, making it a function of the frequency width and central frequency of the wave packet, (c) showing . that at high frequencies correlation techniques do not provide the shortest travel time between two spatial locations, (d) in averaging the signal to improve signal to noise ratio, the assumption that travel time of the averaged signal is equal to the average of the individual travel times is erroneous, (e) Duvall's law of traditional helioseismology is equivalent to the phase time-distance curve; the two are connected through a simple transformation. The result is the analytic inversion of local radial sound speed.

These contributions could lead to a reliable understanding of the local and global structures in the solar interior, particularly sunspots and the mechanisms that drive the numerous phenomena at and above the surface of the Sun.

Time-distance helioseismology is a method to study the interior of the Sun by computing travel time of individual acoustic wavepackets as they travel through the Sun between two spatially separated locations on its surface. I have contributed to the theoretical development of this field.
eg. Theoretical Foundations of Time-Distance Helioseismology

Helioseismic tomography is a form of the tomographic techniques adapted to image the interior of the Sun. The important adaptation is the computation of travel time through time-distance helioseismology. Though the technique has a long history in various other fields its adaptation in studying the solar interior has difficulties. I have contributed in the aspects of its adaptation and improvement.

Helioseismic tomography is a form of the tomographic techniques adapted to image the interior of the Sun from observations of the acoustic oscillations at the surface. The important adaptation is the computation of travel time through time-distance helioseismology. I have contributed in the aspects of its adaptation and improvement.
eg. A Note on Helioseismic Tomography

The magnetic fields of the Sun are known to drive a myriad of phenomena from sunspots to solar flares. Sunspots are among the most prominently visible surface magnetic features. They are known to be produced by magnetic flux tubes that emerge through the surface. The progenitors of all magnetic features - the magnetic flux tubes - are commonly accepted to be the product of the dynamo action that is believed to operate in the deep interior of the Sun at a depth of roughly 200,000 km. The study of the dynamics of sunspots has attracted a large number of investigators. However, we have yet to reach a complete understanding of their origin, formation, morphology and dynamics.

To understand the morphology and dynamics of sunspots we studied the dynamics of their progenitors. Magnetic flux tubes have to traverse a highly turbulent convectively unstable region before they can produce the sunspots at the surface. We modeled the flux tube to be a one-dimensional string with all properties of a magnetic flux tube allowed to move in the three-dimensional space of the convection zone. We could successfully explain a number of dynamical and morphological properties of sunspots.

Most importantly, to explain these surface properties of sunspots we found that the magnetic field strength had to be 100,000 G at the base of the convection zone. This is an order of magnitude larger than the magnetic field strength that can be in energy equipartition with the turbulent motions.

This study involves the dynamics of their progenitors -- magnetic flux tubes --- from the region
of their origin (200,000 km beneath the solar surface) through a highly turbulent convectively unstable region. We modeled the flux tube to be a one-dimensional string with all properties of a magnetic flux tube allowed to move in the three-dimensional space of the convection zone. We could successfully explain a number of dynamical and morphological properties of sunspots if the magnetic field strength of the flux tubes at the region of their origin were of the order of 100,000 G. This is order of magnitude larger than the field that would be in energy equipartition with the turbulent motions.A Theoretical Model for Tilts of Bipolar Magnetic Regions